Miss Lawrence, who worked in a kitchen at York University and was 35 when she went missing, has not been seen since 2009. Police believe she has been murdered.

Claudia Lawrence has not been seen since 2009

Det Supt Malyn said: "I know people have lied to us. We already arrested one person on suspicion of perverting the course of justice and I will continue to arrest people, where there's a legal basis, if I believe they're lying to me."

The detective added: "Whilst the favoured theory is that she left for work in the morning, due to the missing property, you can't eliminate, until somebody tells me otherwise, that she many have come to some harm in the house.

"If she came to some harm in the house during the hours of darkness, the obvious route, for me, the suspect will have taken to get away without being noticed would be down the alleyway."

“People may lie because they are in a relationship, and there could be number of reasons why they are withholding information.

“One of the motives for not coming forward already is because they might be in a relationship with Claudia and don’t want people to find out.

Miss Lawrence's father Peter says the idea police have been lied to about his daughter's appearance is 'dreadful'

“We have significant leads, my team, and myself are determined that if anybody is lying to us we will be arresting people because I am convinced people have information which they are not telling us about.

“We need to eliminate people who have previously not come forward.”

North Yorkshire Police began reviewing the case in 2013 and have since carried out a number of searches, including a detailed re-examination of Miss Lawrence's house in the Heworth area of the city.

On Wednesday, the alley behind the house was cordoned off and specialist officers could be seen on their knees, conducting a fingertip search. An officer with a dog was also involved in the operation.

Police believe Miss Lawrence has been murdered

Det Supt said: "The review remains very active and the team are currently working on a lead that may indicate the alleyway at the rear of Claudia's house is significant.

"We still don't know if Claudia left for work on the morning of Thursday March 19 2009 or whether something happened overnight within her house.

“If the latter is the case, the person or persons responsible, in my view, would have used the rear alleyway as the front door leads on to a busy main road. This is why this specific piece of information needs to be fully investigated.

"The activity today focuses on the alleyway with search-trained officers and a dog. Officers will be conducting house-to-house inquiries in the vicinity to jog people's memories about any vehicular access to the alleyway and how frequently this was used by neighbours or other pedestrians.

"This includes contacting people who have since moved away from the area to assist the investigation. We are also checking again that no CCTV recording equipment in the neighbourhood has been overlooked."

Miss Lawrence’s father Peter said it was “dreadful” that people may have been lying to police investigating his daughter’s disappearance.

He said: "I heard that and it's obviously absolutely dreadful that anyone would do that.

"We know that people lie to the police but in a case like this that involves Claudia's disappearance and everyone can see what it's done to the family ... come on."

This week would have been Miss Lawrence’s 41st birthday.

Det Supt Malyn added: "This is a very poignant week for Claudia's family and friends as they should be celebrating her 41st birthday on Friday, rather than marking another upsetting milestone since she disappeared almost six years ago.

"Our thoughts are with her loved ones at this difficult time and as we approach the sixth anniversary of the investigation next month."

Speaking at his house in York, Mr Lawrence said: "The police told me that they were going to be down there because they thought there was significance in the alleyway at the rear of the house - basically that's all I know.

"It's a criminal investigation and they need to be careful about what they say.

"I think it's just positive that they are looking, They've got a team out and they're still active and it keeps it in the public eye."

Mr Lawrence said: "We all know that somebody out there does know what happened to Claudia."

He said: "Somebody clearly does know what happened and maybe from a misguided sense of loyalty they've kept quiet. Hopefully this very thorough investigation, and keeping it in the public, will make them change their mind."

Mr Lawrence said: "Friday is Claudia's 41st birthday, so that's the sixth birthday that we've had to do without her company and her jollity. It's a long time.

"It's difficult all the time but when there's a birthday, when you get the anniversaries and at Christmas it's just worse. Claudia ought to be with us. How might she have changed in six years? What have we missed in all that time?"